Problem: Solve for $x$ and $y$ using elimination. ${2x+3y = 19}$ ${-2x+2y = -14}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $5y = 5$ $\dfrac{5y}{{5}} = \dfrac{5}{{5}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {2x+3y = 19}\thinspace$ to find $x$ ${2x + 3}{(1)}{= 19}$ $2x+3 = 19$ $2x+3{-3} = 19{-3}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 1}$ into $\thinspace {-2x+2y = -14}\thinspace$ and get the same answer for $x$ : ${-2x + 2}{(1)}{= -14}$ ${x = 8}$